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y=C/(x+1) ( I get it from sol=DSolve[y'[x]==-y[x]/(x+1),y[x],x]) How I can plot this “sol” with showing tangets in list of points ?Read more

I am a first reader of Differential Equation. I was solving a differential equation whose solution is $ |f(x)|= c$ . Now my question is can I write that the solution is $ f(x)= k$ . If $ f(x)$ is continuous then I can remove the mod. But I am not sure whether the functionRead more

Assume that $ J$ is an almost complex structure on torus $ \mathbb{T}^2$ . Let $ X$ be a non vanishing vector field on the torus. Let $ g$ be a Riemannian metric with corresponding $ LC$ connection $ \nabla$ . We define the following differential operator on $ \chi^{\infty}(\mathbb{T}^2)$ , the space of smoothRead more

I’ve done an experiment where I swung a pendulum under air resistance. Is it possible to model the data using the following differential equation and find a b-value? (y”[x])+ Sin[y[x]] + b(y'[x]) == 0, y[0] == 1.5, y'[0] == 0}, y, {x, 0, 3*Pi}]Read more

I am trying to solve following PDE’s for functions Xt,Xx,Xy using DSolve but to no avail- killing={2(Xt^(1,0,0))[t,x,y]==0 ,(Xt^(0,1,0))[t,x,y]+(Xx^(1,0,0))[t,x,y]==0 ,(Xt^(0,0,1))[t,x,y]+(Xy^(1,0,0))[t,x,y]==0 ,2(Xx^(0,1,0))[t,x,y]==0 ,(Xx^(0,0,1))[t,x,y]+(Xy^(0,1,0))[t,x,y]==0 ,2(Xy^(0,0,1))[t,x,y]==0}; DSolve[killing, {Xt[t, x, y], Xx[t, x, y], Xy[t, x, y]}, {t, x, y}]; Can anyone help me figure out the problem.Read more

I have a problem with the solution of this PDE, how can I start to solve it? $ \left(\partial_x^2 + \frac{1}{x}\partial_x + \partial_y^2 \right) F(x,y) = \frac{4\pi I}{x} \left(\frac{\sqrt{x^2+(y\pm M)^2}-2M} {\sqrt{x^2+(y\pm M)^2}+2M}\right)^{1/2}\delta(x-x_0)\delta(y-y_0) $ where $ I$ and $ M$ are the positive constants.Read more

I have the following set of 14 differential equations with the variables listed. When I run it, a message comes “Repeated convergence test failure..” \[Alpha] = 1.5; \[CapitalDelta]1 = 2 \[Pi]*1.45*10^6; \[CapitalDelta]2 = 2 \[Pi]*1.45*10^6; k1 = 2 \[Pi]*759*10^3; k2 = 2 \[Pi]*759*10^3; g1[k1_, k2_, \[Alpha]_] = \[Alpha]/4 (k1 + k2); A1[k1_, \[CapitalDelta]1_] = (I*k1)/2Read more

Let $ E \subset H \subset E^{*}$ , where $ E$ is a real Banach space, $ E^{*}$ its dual and $ H$ is a real Hilbert space. Embendings are continuous and dense. Let $ \langle v_1,v_2\rangle$ be a dual pair for $ v_1 \in E^{*}, v_2 \in E$ . An operator (nonlinear, in general)Read more

Here is a 3rd order nonlinear ODE: $ $ H^2(H_{\eta\eta\eta}-\eta^{-2}H_\eta+\eta^{-1}H_{\eta\eta})-\frac{\eta}{10}=0,$ $ which is subject to the boundary conditions: $ H(0)=1$ and $ H_{\eta\eta}(0)=-c$ with $ c$ being a constant. Now, if one wants to seek a solution $ H(\eta)$ that is an even function in $ \eta$ . My 1st question is: Is there anyRead more

A slightly less general version of this question was asked, in a subsequent comment, by the OP of the question at Controlling subsolutions of a second order linear ODE Let $ f:[0,\infty) \to \mathbb{R}$ obey the differential inequality \begin{equation} f” – 2a f’ + (a^2+b^2) f \le 0,\tag{*} \end{equation} where $ a\in\mathbb R$ and $Read more